Problem set 7
VIK1299
Chapter7-StocksStockValuationandStockMarketEquilibrium..pptxCorporate Valuation and Stock Valuation
CHAPTER 7
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Topics in Chapter
Features of common stock
Valuing common stock
Dividend growth model
Free cash flow valuation model
Market multiples
Preferred stock
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Corporate Valuation and Stock Valuation
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Common Stock: Owners, Directors, and Managers
Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Since managers are “agents” of shareholders, their goal should be: Maximize stock price.
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Classified Stock
Classified stock has special provisions for each class, usually involving voting rights and dividend rights.
Usually named Class A, Class B, etc.
New shares in IPO sometimes have voting restrictions but full dividend rights.
Founders’ shares usually have voting rights but dividend restrictions.
Standard & Poor’s no longer allows new additions to its indices to have classified stock.
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Tracking Stock
The dividends of tracking stock are tied to a particular division, rather than the company as a whole.
Investors can separately value the divisions.
Its easier to compensate division managers with the tracking stock.
But tracking stock usually has no voting rights, and the financial disclosure for the division is not as regulated as for the company.
Very few companies have tracking stock.
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Different Approaches for Valuing Common Stock
Free cash flow model
Constant growth
Nonconstant growth
Dividend growth model
Constant growth
Nonconstant growth
Using the multiples of comparable firms
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The Free Cash Flow Valuation Model: FCF and WACC
Free cash flow (FCF) is:
The cash flow available for distribution to all of a company’s investors.
Generated by a company’s operations.
The weighted average cost of capital (WACC) is:
The overall rate of return required by all of the company’s investors.
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Value of Operations (Vop)
The PV of expected future FCF, discounted at the WACC, is the value of a company’s operations (Vop):
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Sources of Value
Value of operations
Nonoperating assets
Short-term investments and other marketable securities
Ownership of non-controlling interest in another company
Value of nonoperating assets usually is very close to figure that is reported on balance sheets.
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Claims on Corporate Value
Debtholders have first claim.
Preferred stockholders have the next claim.
Any remaining value belongs to stockholders.
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Total Corporate Value: Sources and Claims
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Value of operations= PV of FCF discounted at WACC
Conceptually correct, but how do you find the present value of an infinite stream?
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Suppose FCFs are expected to grow at a constant rate, gL, starting at t=1, and continue forever. What happens to FCF?
What is the value of operations if FCFs grow at a constant rate? See next slide.
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Value of operations in terms of FCF1 and gL:
We can multiply and divide by (1+gL), for a reason that will soon be clear, as shown on the next slide.
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Rewritten value of operations:
We can group , as shown on the next slide.
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Value of operations with grouped terms:
We can group the terms, as shown on the next slide.
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Value of operations if FCF grows at a constant rate:
What happens toif t gets large? It depends on the size of gL relative to WACC. See next slide.
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What happens to as t gets large?
If gL < WACC: Then < 1.
If gL ≥ WACC: Then ≥ 1.
What happens to the value of operations if gL ≥ WACC? See next slide.
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What happens to the value of operations if gL ≥ WACC?
Vop = (Big) + (Bigger) + (Even Bigger) + …+ (Really big!) = Infinity! So g can’t be greater than or equal to WACC!
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What happens to the value of operations if gL ≤ WACC?
Vop = (Small) + (Smaller) + (Even smaller) + …+ FCF0 (Really small!) = ?
All the terms get smaller and smaller, but what happens to the sum? See next slide
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What is the sum of an infinite number of factors that get smaller at a geometric rate?
Consider this example. The first row is t. The second row is a number that is less than 1 that is compounded to the power of t. The third row is the cumulative sum.
| t | 1 | 2 | 3 | 4 | . . . ∞ |
| (1/2)t | 1/2 | 1/4 | 1/8 | 1/16 | 1/∞ ≈ 0 |
| Σ(1/2)t | 1/2 | 3/4 | 7/8 | 15/16 | ≈ 1 |
This sum converges to 1. Similarly, converges (although not to 1). See next slide.
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Constant Growth Formula for Value of Operations: gL begins at Time 1
If FCF are expected to grow at a constant rate of gL from Time 1 and afterwards, and gL<WACC:
This is the PV of all FCF from Time 1 through infinity, when discounted at WACC.
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Constant Growth Formula for Value of Operations: gL begins at Time 0
If FCF are expected to grow at a constant rate of gL from Time 0 and afterwards, and gL<WACC:
This is still the PV of all FCF from Time 1 through infinity, when discounted at WACC.
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Data for FCF Valuation
FCF0 = $24 million
WACC = 11%
FCF is expected to grow at a constant rate of gL = 5%
Short-term investments = $100 million
Debt = $200 million
Preferred stock = $50 million
Number of shares =n = 10 million
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Find Value of Operations
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Total Value of Company (VTotal)
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Estimated Intrinsic Value of Equity (VEquity)
| Voperations | $420.00 |
| + ST Inv. | 100.00 |
| VTotal | $520.00 |
| −Debt | 200.00 |
| − Preferred Stk. | 50.00 |
| VEquity | $270.00 |
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Estimated Intrinsic Stock Price per Share, (1 of 2)
| Voperations` | $420.00 |
| + ST Inv. | 100.00 |
| VTotal | $520.00 |
| −Debt | 200.00 |
| − Preferred Stk. | 50.00 |
| VEquity | $270.00 |
| n | 10 |
| $27.00 |
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Expansion Plan: Nonconstant Growth
Finance expansion financed by owners.
Projected free cash flows (FCF):
Year 1 FCF = −$10 million.
Year 2 FCF = $20 million.
Year 3 FCF = $35 million
FCF grows at constant rate of 5% after year 3.
No change in WACC, marketable securities, debt, preferred stock, or number of shares of stock.
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Estimating the Value of Operations
Free cash flows are forecast for three years in this example, so the forecast horizon is three years.
Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.
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Time Line of FCF
| Year | 0 | 1 | 2 | 3 | 4 | 5 | … t |
| FCF | −$10 | $20 | $35 | FCF3(1+gL) | FCF4(1+gL) | FCFt(1+gL) |
Free cash flows are forecast for three years in this example, so the forecast horizon is three years.
Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.
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Horizon Value
| Year | 0 | 1 | 2 | 3 | 4 | 5 | … t |
| FCF | FCF3(1+gL) | FCF4(1+gL) | FCFt(1+gL) | ||||
| HV3 | ← ↵ | ← ↵ | ← ↵ |
Horizon value is also called terminal value, or continuing value.
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Horizon Value Application (FCF3 = $35, WACC = 11%, gL = 5%)
This is the value of FCF from Year 4 and beyond discounted back to Year 3.
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Value of Operations at t=0: PV of FCF1 through FCF3 plus PV of HV3
| Year | 0 | 1 | 2 | 3 | 4 | 5 | … t |
| FCF | FCF1 | FCF2 | FCF3 | ||||
| PV of FCF in explicit forecast | ← ↵ | ← ↵ | ← ↵ | FCF3(1+gL) | FCF4(1+gL) | FCFt(1+gL) | |
| + | HV3 | ← ↵ | ← ↵ | ← ↵ | |||
| PV of HV | ← ↵ | ← ↵ | ← ↵ | ||||
| = Value of operations Time 0 |
PV of HV is the PV of FCF beyond the explicit forecast. So PV of HV plus PV of FCF in explicit forecast is the PV of all future FCFs.
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Application: Current Value of Operations (Nonconstant g in FCF until after Year 3; gL = 5%; WACC = 11%)
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Estimated Intrinsic Stock Price per Share, (2 of 2)
| Voperations | $480.67 |
| + ST Inv. | 100.00 |
| VTotal | $580.67 |
| −Debt | 200.00 |
| − Preferred Stk. | 50.00 |
| VEquity | $330.67 |
| ÷ n | 10 |
| $33.07 |
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How much of the value of operations is based on cash flows from Year 4 and beyond?
The horizon value is the value of all FCF from Year 4 and beyond, discounted back to Year 3.
The present value of HV3 is the present value of all FCF from Year 4 and beyond.
The PV of HV3 is the percent of total value due to long-term cash flows.
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Value of Operations and Present Value of Horizon Value
Value of operations: Vop = $480.67
Horizon value: HV3 = $612.5
PV of HV3 = $612.5/(1 + 0.11)3
= $447.855
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Percent of Value Due to Long-Term Cash Flows
In this example, 93% of value is due to cash flows 4 or more years into the future.
For the average company, this percentage is around 80%.
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Long-term versus Short-term Focus
Why focus on quarterly earnings if most value is from longer-term cash flows?
Changes in quarterly earnings can signal changes future in cash flows. This would affect the current stock price.
Managers often have bonuses tied to quarterly earnings, so they have incentive to manage earnings.
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Forecasting Free Cash Flows: A Simple Approach
Forecast sales to grow at chosen growth rates.
Forecast net operating profit after taxes (NOPAT) and total net operating capital (OpCap) as a percent of sales.
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Current Situation (in millions)
Most recent data:
Sales of $2,000
Total net operating capital, OpCap = $1,120
Operating profitability ratio
OP = NOPAT/Sales = 4.5%
Capital requirement ratio
CR = OpCap/Sales = 56%.
The target weighted average cost of capital (WACC) is 9%.
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Initial Operating Assumptions for the No Change Scenario
Operating ratios remain unchanged from values in most recent year.
Sales will grow by 10%, 8%, 5%, and 5% for the next four years.
The long-term growth rate in sales is 5%.
The target weighted average cost of capital (WACC) is 9%.
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Assumptions
| Actual | Forecast | ||||
| Inputs | 0 | 1 | 2 | 3 | 4 |
| WACC | 9.0% | ||||
| Sales | $2,000 | ||||
| OpCap | $1,120 | ||||
| Sales growth rate | 10% | 8% | 5% | 5% | |
| NOPAT/Sales | 4.5% | 4.5% | 4.5% | 4.5% | 4.5% |
| OpCAP/Sales | 56.0% | 56.0% | 56.0% | 56.0% | 56.0% |
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Examples of Forecasting Items
Sales1 = $2,000(1+0.10) = $2,200
NOPAT1 = $2,200(0.045) = $99
OpCap1 = $2,200(0.56) = $1,232
FCFt = NOPATt − (OpCapt − OpCapt-1)
ROICt = NOPATt/OpCapt
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Forecasted FCF: No changes in operating ratios
| Scenario: No Change | Actual | Forecast | |||
| 0 | 1 | 2 | 3 | 4 | |
| Sales | $2,000 | $2,200 | $2,376 | $2,495 | $2,620 |
| NOPAT | $99 | $107 | $112 | $117.879 | |
| OpCap | $1,120 | $1,232 | $1,331 | $1,397.088 | $1,466.942 |
| FCF | −$13 | $8.36 | $45.738 | $48.025 | |
| Growth in FCF | -164% | 447.1% | 5.0% | ||
| ROIC | 8.0% | 8.0% | 8.0% | 8.0% | 8.0% |
FCF is negative in Year 1.
ROIC of 8% is less than WACC of 9%--not good!
Note: There is no rounding in intermediate calculations.
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Estimated Intrinsic Value (1 of 2)
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Estimated Intrinsic Value (2 of 2)
| Scenario: No Change | |
| Horizon Value: | |
| HV4 = | $1,260.65 |
| Value of Operations: | |
| Present value of HV | $893.08 |
| + Present value of FCF | $64.45 |
| Value of operations ≈ | $958 |
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The Value of Operations versus the Total Net Operating Capital
The ROIC (8%) is too low compared to the WACC (9%).
The capital is not earning enough to meet investors’ required return, so:
Horizon value ($958) is less than the total net operating capital at the horizon ($1,467).
Current value of operations ($958) is less than the current total net operating capital ($1,120).
ROIC must be greater than WACC/(1+gL) for horizon value to be greater than the total net operating capital at the horizon.
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Value Drivers
The ROIC (8%) is too low compared to the WACC (9%).
The capital is not earning enough to meet investors’ required return, so:
Horizon value ($958) is less than the total net operating capital at the horizon ($1,467).
Current value of operations ($958) is less than the current total net operating capital ($1,120).
ROIC must be greater than WACC/(1+gL) for horizon value to be greater than the total net operating capital at the horizon.
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Impact of Higher Growth Rates
| No Change | Improve Growth | |
| g0,1 | 10% | 11% |
| g1,2 | 8% | 9% |
| g2,3 | 5% | 6% |
| g3,4 | 5% | 6% |
| gL | 5% | 6% |
| OP | 4.5% | 4.5% |
| CR | 56.0% | 56.0% |
| ROIC | 8.0% | 8.0% |
| Vop,0 | $958 | $933 |
| WACC | 9.00% | 9.00% |
Higher growth causes Vop,0 to fall.
ROIC must be greater than WACC/(1+WACC) for growth to add value.
WACC/(1+WACC) = 8.26%
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Impact of Higher Operating Profitability
| No Change | Improve OP | |
| g0,1 | 10% | 10% |
| g1,2 | 8% | 8% |
| g2,3 | 5% | 5% |
| g3,4 | 5% | 5% |
| gL | 5% | 5% |
| OP | 4.5% | 5.5% |
| CR | 56.0% | 56.0% |
| ROIC | 8.0% | 9.8% |
| Vop,0 | $958 | $1,523 |
| WACC | 9.00% | 9.00% |
Higher operating profitability increases the ROIC.
ROIC of 9.8% > 8.26%
The higher ROIC causes a big increase in Vop,0.
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Impact of Lower Capital Requirements
| No Change | Improve CR | |
| g0,1 | 10% | 10% |
| g1,2 | 8% | 8% |
| g2,3 | 5% | 5% |
| g3,4 | 5% | 5% |
| gL | 5% | 5% |
| OP | 4.5% | 4.5% |
| CR | 56.0% | 51.0% |
| ROIC | 8.0% | 8.8% |
| Vop,0 | $958 | $1,191 |
| WACC | 9.00% | 9.00% |
Lower capital requirements increases the ROIC.
ROIC of 8.8% > 8.26%
The higher ROIC causes an increase in Vop,0.
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Impact of Simultaneous Improvements in OP and CR
| No Change | Improve OP and CR | |
| g0,1 | 10% | 10% |
| g1,2 | 8% | 8% |
| g2,3 | 5% | 5% |
| g3,4 | 5% | 5% |
| gL | 5% | 5% |
| OP | 4.5% | 5.5% |
| CR | 56.0% | 51.0% |
| ROIC | 8.0% | 10.8% |
| Vop,0 | $958 | $1,756 |
| WACC | 9.00% | 9.00% |
The ROIC is much higher due to the improvements in operations.
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Impact of Simultaneous Improvements in Growth, OP, and CR
| No Change | Improve All | |
| g0,1 | 10% | 11% |
| g1,2 | 8% | 9% |
| g2,3 | 5% | 6% |
| g3,4 | 5% | 6% |
| gL | 5% | 6% |
| OP | 4.5% | 5.5% |
| CR | 56.0% | 51.0% |
| ROIC | 8.0% | 10.8% |
| Vop,0 | $958 | $2,008 |
| WACC | 9.00% | 9.00% |
The ROIC is much higher due to the improvements in operations.
With a higher ROIC, growth adds substantial value.
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Summary: Value of operations for previous combinations of ROIC and gL
| ROIC | ROIC | ROIC | ROIC | ROIC | |
| 8.0% | 8.8% | 9.8% | 10.8% | ||
| gL | 5% | $958 | $1,191 | $1,523 | $1,756 |
| gL | 6% | $933 | $1,247 | $1,694 | $2,008 |
The ROIC is much higher due to the improvements in operations.
With a higher ROIC, growth adds substantial value.
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Are volatile stock prices consistent with rational pricing?
The previous slide shows that small changes in ROIC and growth cause large changes in value.
Similarly, small changes in the cost of capital (WACC), perhaps due to changes in risk or interest rates, cause large changes in value.
As new information arrives, investors continually update their estimates of operating profitability, capital requirements, growth, risk, and interest rates.
If stock prices aren’t volatile, then this means there isn’t a good flow of information.
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Value of dividend-paying stock = PV of dividends discounted at required return
Conceptually correct, but how do you find the present value of an infinite stream?
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Suppose dividends are expected to grow at a constant rate, gL, forever.
D1 = D0(1 + gL)1
D2 = D0(1 + gL)2
Dt = D0(1 + gL)t
What is the present value of a constant growth Dt when discounted at the stock’s required return, rs? See next slide.
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Present Value of a Constant Growth Dividend
What happens to as t gets bigger?
If gL<rs: Then < 1.
So the bracket approaches zero as t gets large.
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Constant Dividend Growth Model (gL<rs)
If gL is constant and less than rs, then converges to:
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What happens if gL > rs?
So gL must be less than rs for the constant growth model to be applicable!!
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Required rate of return: beta = 1.2, rRF = 7%, and RPM = 5%.
Use the SML to calculate rs:
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Estimated Intrinsic Stock Value: D0 = $2.00, rs = 13%, gL = 6%
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Expected Stock Price in 1 Year
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Expected Dividend Yield and Capital Gains Yield (Year 1)
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Total Year 1 Return
Total return = Dividend yield + Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = gL.
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Rearrange model to rate of return form:
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Nonconstant Growth Stock
Nonconstant growth of 30% for Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant gL = 6%.
Can no longer use constant growth model.
However, growth becomes constant after 3 years.
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Steps to Estimate Current Stock Value
Forecast dividends for nonconstant period, which ends at horizon date after which growth is constant at gL.
Find horizon value, which is PV of dividends beyond horizon date discounted back to horizon date
Horizon value = =
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Steps to Estimate Current Stock Price (Continued)
Find PV of each dividend in the forecast period.
Find PV of horizon value.
Sum PV of dividends and PV of horizon value.
Result is estimated current stock value.
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Example of Estimating Current Stock Value (D0 = $2.00, rs = 13%)
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